# A2.S.5: Normal Distributions: Know and apply the characteristics of the... distribution ```Regents Exam Questions A2.S.5: Normal Distributions 5
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A2.S.5: Normal Distributions: Know and apply the characteristics of the normal
distribution
1 The scores on a test have a normal distribution.
The mean of the scores is 40 and the standard
deviation is 6. The probability that a score
chosen at random lies between 34 and 46 is
closest to
1) .34
2) .68
3) .95
4) .99
5 The amount of time that a teenager plays video
games in any given week is normally
distributed. If a teenager plays video games an
average of 15 hours per week, with a standard
deviation of 3 hours, what is the probability of
a teenager playing video games between 15
and 18 hours a week?
6 A shoe manufacturer collected data regarding
men’s shoe sizes and found that the distribution
of sizes exactly fits the normal curve. If the
mean shoe size is 11 and the standard deviation
is 1.5, find:
a the probability that a man’s shoe size is
greater than or equal to 11
b the probability that a man’s shoe size is
greater than or equal to 12.5
2 The average score for a Latin test is 77 and the
standard deviation is 8. Which percent best
represents the probability that any one student
scored between 61 and 93 on the test?
1) 95%
2) 99.5%
3) 68%
4) 34%
c
3 If the amount of time students work in any
given week is normally distributed with a mean
of 10 hours per week and a standard deviation
of 2 hours, what is the probability a student
works between 8 and 11 hours per week?
1) 34.1%
2) 38.2%
3) 53.2%
4) 68.2%
4 A set of normally distributed student test scores
has a mean of 80 and a standard deviation of 4.
Determine the probability that a randomly
selected score will be between 74 and 82.
Regents Exam Questions A2.S.5: Normal Distributions 5
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1 ANS: 2
2 ANS: 1
3 ANS: 3
REF: 011212a2
4 ANS:
.624
REF: 010226b
5 ANS:
0.341
REF: 080222b
6 ANS:
0.5, 0.159,
REF: 010327b
REF: 068527siii
REF: 010131siii
```